Question

Simplify: $\sqrt[3]{3\frac{216}{2197}}$.

• A. $\frac{36}{27}$
• B. $\frac{66}{23}$
• C. $\frac{6}{13}$
• D. None of the above
  

Answer 1

The correct option is C $\frac{6}{13}$

On prime factorisation of the numbers individually, we get,

$216=\underset{–}{2\times 2\times 2}\times \underset{–}{3\times 3\times 3}=2^3\times 3^3=6^3$.

$2197=\underset{–}{13\times 13\times 13}={13}^3$.

Therefore,

$\sqrt[3]{3\frac{216}{2197}}$$=\frac{\sqrt[3]{3216}}{\sqrt[3]{32197}}$ $=\frac{\sqrt[3]{36^3}}{\sqrt[3]{3{13}^3}}$ $=\frac{6}{13}.$

Thus, option $C$ is correct.